S. Rao Aiyagari: My Student and My Teacher (P

Federal Reserve Bank of Minneapolis

S. Rao Aiyagari: My Student and My Teacher (p. 2) Neil Wallace

Reprints

Deflating the Case for Zero Inflation (p. 5) S. Rao Aiyagari On the Contribution of Technology Shocks to Business Cycles (p. 15) S. Rao Aiyagari Macroeconomics With Frictions (p. 28) S. Rao Aiyagari

The Published Work of S. Rao Aiyagari (p. 45) Federal Reserve Bank of Minneapolis Quarterly Review vw.21.no. 3 ISSN 0271-5287

This publication primarily presents economic research aimed at improving policymaking by the Federal Reserve System and other governmental authorities. Any views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

Editor: Arthur J. Rolnick Associate Editors: Edward J. Green, Preston J. Miller, Warren E. Weber Economic Advisory Board: Beth Allen, Lawrence J. Christiano, Edward C. Prescott, James A. Schmitz, Jr., Neil Wallace Managing Editor: Kathleen S. Rolfe Article Editors: Kathleen A. Mack, Kathleen S. Rolfe, Jenni C. Schoppers, Martha L. Starr Designer: Phil Swenson Typesetters: Mary E. Anomalay, Jody Fahland, Correan M. Hanover Circulation Assistant: Elaine R. Reed

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S. Rao Aiyagari: My Student and My Teacher

Neil Wallace* Adviser Research Department Federal Reserve Bank of Minneapolis and Professor of Economics Pennsylvania State University

In 1976, when S. Rao Aiyagari applied to the University Rao'sfirst substantial body of research work in eco- of Minnesota graduate program in economics, I was in nomics, begun at Wisconsin and completed during the first charge of admissions. As I reviewed his application, I re- few years of his stay at the Minneapolis Fed, was a far member being impressed by the fact that he had already more general treatment of the topic of hisfirst economics published a paper in physics: "On the Equivalence of the paper, the relationship between models of overlapping gen- Einstein-Mayer and Einstein-Cartan Theories for Describ- erations and models of infinitely lived people. Among the ing a Spinning Medium" (Aiyagari and Mahanta 1975). questions he addressed were whether the two models be- Minnesota accepted Rao as a graduate student in econom- come similar if the length of life of each generation and the ics, and he did not disappoint us; he was one of the stars period of overlap are sufficiently great or if the generations of the program. Although I was Rao's adviser, he worked are linked through altruism between parents and children. independently, and I remember thinking then that I could Rao's fundamental theoretical work in this area may be his learn a lot more from him than he from me. That judg- most important legacy to the economics profession. (See ment held firm the rest of his life, as hefinished hi s thesis Aiyagari 1987, 1988, 1989, 1992a, and 1992b; and Aiya- and we became colleagues and friends. gari and Peled 1991.) Rao'sfirst published economics paper, which grew out Around 1990, Rao turned primarily toward applied of his thesis, was entitled "Observational Equivalence of work. He wanted to solve outstanding quantitative puz- the Overlapping Generations and the Discounted Dynamic zles, like the extent to which the average real yield on eq- Programming Frameworks for One-Sector Growth" (Aiya- uities exceeds that on U.S. Treasury bills (the equity pre- gari 1985). The similarity in titles between this and his mium puzzle). And he wanted to provide the most con- physics paper suggests that Rao was applying to econom- vincing possible analyses of important policy issues. (See ics the scientific method that he had used in physics. This, Aiyagari 1994a, 1994b, and 1995; Aiyagari and Gertler indeed, was his approach, and he used it throughout his 1991; and Aiyagari and Peled 1995.) The three Quarterly career. Review articles reprinted in this issue reflect that shift in Rao'sfirst positio n after graduate school was in the Economics Department at the University of Wisconsin, Madison. In 1986, after five year s there, he left to join the *Here, as has been true with most of my writing for the Quarterly Review, I have received invaluable help from Kathy Rolfe. Her help is especially appropriate and wel- Research Department at the Federal Reserve Bank of Min- come in the preparation of my introduction to this memorial issue of the Quarterly neapolis. He remained there until about a year ago. Review because Kathy also worked closely with Rao.

2 Neil Wallace S. Rao Aiyagari

his work. Thefirst reprinte d article, "Deflating the Case economic research conferences sponsored by the Minneap- for Zero Inflation" (p. 5), is based largely on the research olis Fed. He scored his greatest success—both as a con- of others, but it illustrates how Rao went about analyzing ference organizer and as a forecaster—by holding a con- an important policy issue, one that remains controversial ference in 1995 in honor of the 25th anniversary of the today. The article applies to that issue a much wider range date Robert E. Lucas, Jr., submitted for publication what of perspectives than such analyses usually include, and it turned out to be an extremely influential paper. (The paper reaches a conclusion that can hardly be called popular. was submitted in 1970 and published in 1972.) Just a few The second reprinted article, "On the Contribution of months after the conference, Lucas was awarded the Nobel Technology Shocks to Business Cycles" (p. 15), displays Prize for work for which that paper is the centerpiece. the highly original way Rao was able to bring evidence to The main recognition Rao sought, however, was the bear on theories. That article makes new and important offer of a position at a leading academic economics de- points about the kinds of models that can hope to simulta- partment. That came last year when he was invited to be- neously explain the cyclical patterns of the average real come a full professor in the Economics Department at the wage and aggregate labor productivity. The third reprinted University of Rochester, New York, one of the strongest article, "Macroeconomics With Frictions" (p. 28), plays a departments in macroeconomics in the country. The offer special role in this memorial issue; besides being a mas- came after Rao had spent the autumn of 1995 visiting the terful introduction to a large body of work, it contains Rochester department; when it came, he accepted it imme- strong hints about where Rao thought his—and the pro- diately. fession's—future research efforts should be concentrated. Rao made no secret of the fact that he was thrilled by Despite Rao's turn toward applied work around 1990, his professorial appointment. He went so far as to describe I convinced him about this time to join me in exploring it as the culmination of his career. It certainly represented models of money related to the 1989 work of Nobuhiro a long-deserved recognition of his ability and accomplish- Kiyotaki and Randall Wright, models which are not di- ments. While his family, his friends, and his colleagues rectly applicable to current policy issues. Our collabora- can take solace in his great happiness during what turned tion and later work which grew from it have been my out to be his brief tenure at Rochester, his colleagues do main research ever since. Rao was an excellent theorist, not agree with Rao that he had reached the culmination of and in the course of working with him, I learned a great his career. Our view, which readers of this issue are likely deal. I continue to explore ideas that we discussed but to share, is that Rao was bursting with ideas and with the were not able to pursue at the time. After several years, energy and skill required to pursue them fruitfully. We will however, Rao concluded that the models we were study- always wonder what more he would have accomplished. ing were not fruitful enough, and he abandoned our work. Mutual friends tell me that he found it extremely difficult to tell me that he felt that way. I regret that I never told him how much I had gained from our collaboration. (See Aiyagari and Wallace 1991, 1992, and 1997; and Aiya- gari, Wallace, and Wright 1996.) Many who knew Rao well viewed him, as I did, as one of the ablest economists of his generation. In the early 1990s, we thought that he was not getting the recognition that he deserved. Fortunately, the situation began to change about three years ago. Rao began to receive many invita- tions to present his work at seminars and conferences at leading economics departments and research institutes, both here and abroad. (Rao loved to travel, and travel seemed to be one of the few casual subjects he liked to talk about. I remember his great enthusiasm after returning from New York City, Israel, Italy, Russia, and Turkey.) During this time, Rao also became the leading organizer of

3 References

S. Rao Aiyagari. 1985. Observational equivalence of the overlapping generations and the discounted dynamic programming frameworks for one-sector growth. Jour- nal of Economic Theory 35 (April): 201-21. . 1987. Optimality and monetary equilibria in stationary overlapping generations models with long-lived agents: Growth versus discounting. Journal of Economic Theory 43 (December): 292-313. . 1988. Nonmonetary steady states in stationary overlapping generations models with long lived agents and discounting: Multiplicity, optimality, and con- sumption smoothing. Journal of Economic Theory 45 (June): 102-27. . 1989. Equilibrium existence in an overlapping generations model with altruistic preferences. Journal of Economic Theory 47 (February): 130-52. . 1992a. Walras' law and nonoptimal equilibria in overlapping generations models. Journal of Mathematical Economics 21: 343-61. . 1992b. Co-existence of a representative agent type equilibrium with a non-representative agent type equilibrium. Journal of Economic Theory 57 (June): 230-36. . 1994a. Frictions in asset pricing and macroeconomics. European Eco- nomic Review 38 (April): 932-39. . 1994b. Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics 109 (August): 659-84. . 1995. Optimal capital income taxation with incomplete markets, bor- rowing constraints, and constant discounting. Journal of Political Economy 103 (December): 1158-75. Aiyagari, S. Rao, and Gertler, Mark. 1991. Asset returns with transactions costs and uninsured individual risk. Journal of Monetary Economics 27 (June): 311-31. Aiyagari, S. Rao, and Mahanta, M. N. 1975. On the equivalence of the Einstein-Mayer and Einstein-Cartan theories for describing a spinning medium. Journal of Math- ematical Physics 16: 381-83. Aiyagari, S. Rao, and Peled, Dan. 1991. Dominant root characterization of Pareto optimality and the existence of optimal equilibria in stochastic overlapping generations models. Journal of Economic Theory 54 (June): 69-83. . 1995. Social insurance and taxation under sequential majority voting and utilitarian regimes. Journal of Economic Dynamics and Control 19 (Novem- ber): 1511-28. Aiyagari, S. Rao, and Wallace, Neil. 1991. Existence of steady states with positive con- sumption in the Kiyotaki-Wright model. Review of Economic Studies 58 (Octo- ber): 901-16. . 1992. Fiat money in the Kiyotaki-Wright model. Economic Theory 2 (October): 447-64. . 1997. Government transaction policy, the medium of exchange, and welfare. Journal of Economic Theory 74 (May): 1-18. Aiyagari, S. Rao.; Wallace, Neil; and Wright, Randall. 1996. Coexistence of money and interest-bearing securities. Journal of Monetary Economics 37 (June): 397-419. Kiyotaki, Nobuhiro, and Wright, Randall. 1989. On money as a medium of exchange. Journal of Political Economy 97 (August): 927-54. Lucas, Robert E„ Jr. 1972. Expectations and the neutrality of money. Journal of Eco- nomic Theory 4 (April): 103-24.